Question

1 question ONLY population proportion help please.

Answer 1

Use a sample n = 840, p^ = 0.25, and a 90% confidence level to construct a confidence interval estimate of the population proportion, p.

A.

0.221 < p < 0.279
B.

0.214 < p < 0.286
C.

0.237 < p < 0.263
D.

0.225 < p < 0.275

Answer 2

i dont know how to find the answer and all i need is to figure this problem out

Answer 3

one sec while I think it over

Answer 4

ive spent 2 hours on this lesson and this is the only one i cant figure out lol

Answer 5

the formula is

\[\Large L = \hat{p} - Z*\sqrt{\frac{p(1-p)}{n}}\]

\[\Large U = \hat{p} + Z*\sqrt{\frac{p(1-p)}{n}}\]

where L is the lower bound of the confidence interval
U is the upper bound

Answer 6

sorry typo

\[\Large L = \hat{p} - Z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]

\[\Large U = \hat{p} + Z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]

ok fixed now

Answer 7

hmm lets see a=0.10 because 90% so a/2=0.05 and 1- 0.05 is 0.95 and so that on the z-chart is 1.645

Answer 8

In this case,

\[\Large \hat{p} = 0.25\]

\[\Large Z = 1.645\]

\[\Large n = 840\]

the value Z = 1.645 is found using the normal distribution. The idea is to find the value of k such that P( -k < Z < k) = 0.90. That value of k is roughly 1.645

Answer 9

yeah you beat me to it lol

Answer 10

lol

Answer 11

so then i plug them into the formula?

Answer 12

correct

Answer 13

ok 1 sec

Answer 14

confused lol

Answer 15

where at?

Answer 16

wouldnt it be E=Za/2 sqrt P^Q^/n

Answer 17

p-hat and q-hat

Answer 18

idk ive never seen the formula you used lol

Answer 19

well q-hat is simply 1 - (p-hat)

Answer 20

\[\Large \hat{q} = 1 - \hat{p}\]

Answer 21

so you can think of

\[\Large L = \hat{p} - Z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]

as

\[\Large L = \hat{p} - Z*\sqrt{\frac{\hat{p} * \hat{q} }{n}}\]

same for the formula for the upper bound U

Answer 22

also, the whole portion from Z to the end of the expression is the margin of error

that's why we have plus or minus that whole mess (plus or minus the margin of error)

Answer 23

So they just said "Let E = Za/2 sqrt(P^Q^/n)"

Answer 24

ohhhhhh

Answer 25

and I'm simplifying things. Instead of saying Za/2, I'm just saying Z

Answer 26

i got a negative lol

Answer 27

hmm

Answer 28

what did you get?

Answer 29

-0.021

Answer 30

xD

Answer 31

for which part?

Answer 32

well i did 0.25-1.6545 for the 1st part of the L

Answer 33

because of P^-Z

Answer 34

what did you get when you computed the square root of p*q/n

Answer 35

0.0149404

Answer 36

because \[\sqrt{0.25}(0.75)/840\]

Answer 37

so you'll have

0.25 - 1.645*0.0149404

for the lower bound L

Answer 38

I think you just calculated 0.25 - 1.645 ?

Answer 39

yeah first

Answer 40

i got 0.225423042 just now for what you said

Answer 41

so it would be 0.226? rounded

Answer 42

0.225

Answer 43

ohhhhh

Answer 44

so that means its D?

Answer 45

to get U, you just change the - to a +

U = 0.25 + 1.645*0.0149404

Answer 46

ok

Answer 47

0.274

Answer 48

0.275*

Answer 49

0.274576958 rounds to 0.275

so yes, D

Answer 50

yay!!

Answer 51

THANKS!! :)

Answer 52

you're welcome

Answer 53

its confusing lol

Answer 54

yeah confidence intervals can be tricky and odd

Answer 55

thats what i was thinking earlier lol thanks again